Finite Group Databasebeta

← C7×#9483 #13186699

Subgroups — C7×#9483 #13186699

Order 1792.

542 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×#2972C211yesmaximal, characteristic
2C7×#2580C211yesmaximal, characteristic
3C7×#1800C211yesmaximal, characteristic
4C7×#1487C212yesmaximal, complemented
5C7×#1286C212yesmaximal, complemented
6C2×C4×C7×Q8C2211yescharacteristic
7C2×C4×C7×D4C2211yescharacteristic
8C7×C8×D4—24no—
9C7×#431C2212yes—
10C7×#423C2212yes—
11C2×C7×#100—21no—
12C2×C7×C22⋊C8—22no—
13C7×#399C412yes—
14C7×#393C412yes—
15C7×#390—21no—
16C7×#389—21no—
17C7×#385—22no—
18C7×#382C2211yescharacteristic
19C7×#343—21no—
20C7×Q8⋊C8—24no—
21#9483C711yesmaximal, characteristic, direct product factor, Sylow
22C22×C7×Q8C2×C411yescharacteristic
23C22×C7×D4D411yescharacteristic
24C23×C4×C7D412yes—
25C2×C7×M16—22no—
26C22×C7×C8—24no—
27C4×C7×Q8—22no—
28C4×C7×Q8—22no—
29C4×C7×D4—22no—
30C4×C7×D4—22no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—21no—
33C2×C7×C4⋊C4—22no—
34C2×C7×C4⋊C4C2×C411yescharacteristic
35C2×C7×C4⋊C4D411yescharacteristic
36C2×C7×C22⋊C4—22no—
37C2×C7×C22⋊C4—22no—
38C2×C7×C22⋊C4C2×C412yes—
39C2×C42×C7—21no—
40C2×C42×C7C2311yescharacteristic
41C7×C4⋊C8—22no—
42C7×C4⋊C8—22no—
43C7×C4⋊C8—22no—
44C7×#100—42no—
45C7×C22⋊C8—24no—
46C7×C22⋊C8—22no—
47C4×C7×C8D414yes—
48C7×#95—22no—
49C7×#95—21no—
50C7×#95C2×C412yes—
51#2972C2×C711yescharacteristic
52#2580C2×C711yescharacteristic
53#1800C2×C711yescharacteristic
54#1487C2×C712yescomplemented
55#1286C2×C712yescomplemented
56C24×C7C22⋊C412yes—
57C2×C7×Q8—22no—
58C2×C7×Q8—42no—
59C2×C7×D4—22no—
60C2×C7×D4—22no—
61C2×C7×D4SD1612yes—
62C2×C7×D4Q1612yes—
63C22×C4×C7—21no—
64C22×C4×C7—22no—
65C22×C4×C7—22no—
66C22×C4×C7—22no—
67C22×C4×C7—21no—
68C22×C4×C7—82no—
69C22×C4×C7C22⋊C412yes—
70C22×C4×C7C22×C411yescharacteristic
71C22×C4×C7C2×D411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C7×M16—42no—
74C7×M16—42no—
75C2×C7×C8—24no—
76C2×C7×C8—42no—
77C2×C7×C8—84no—
78C7×C4⋊C4—22no—
79C7×C4⋊C4—22no—
80C7×C4⋊C4—41no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—42no—
83C7×C4⋊C4—82no—
84C7×C22⋊C4—24no—
85C7×C22⋊C4—44no—
86C7×C22⋊C4—82no—
87C42×C7—42no—
88C42×C7C2×D412yes—
89C42×C7#4112yes—
90C2×C4×Q8C22×C711yescharacteristic
91C2×C4×D4C22×C711yescharacteristic
92C8×D4—24no—
93#431C22×C712yes—
94#423C22×C712yes—
95C2×#100—21no—
96C2×C22⋊C8—22no—
97#399C4×C712yes—
98#393C4×C712yes—
99#390—21no—
100#389—21no—
101#385—22no—
102#382C22×C711yescharacteristic
103#343—21no—
104Q8⋊C8—24no—
105C23×C7—22no—
106C23×C7—22no—
107C23×C7—42no—
108C23×C7—42no—
109C23×C7#10314yes—
110C23×C7C2×C22⋊C411yescharacteristic
111C7×Q8—24no—
112C7×Q8—42no—
113C7×D4—24no—
114C7×D4—24no—
115C2×C4×C7—22no—
116C2×C4×C7—22no—
117C2×C4×C7—41no—
118C2×C4×C7—41no—
119C2×C4×C7—44no—
120C2×C4×C7—41no—
121C2×C4×C7—41no—
122C2×C4×C7—42no—
123C2×C4×C7—42no—
124C2×C4×C7—41no—
125C2×C4×C7—42no—
126C2×C4×C7—41no—
127C2×C4×C7—41no—
128C2×C4×C7—42no—
129C2×C4×C7—82no—
130C2×C4×C7C4×D412yes—
131C2×C4×C7#12011yescharacteristic
132C2×C4×C7#12112yes—
133C2×C4×C7#12311yescharacteristic
134C2×C4×C7C2×SD1611yescharacteristic
135C2×C4×C7C2×Q1611yescharacteristic
136C2×C4×C7#13512yes—
137C7×C8—44no—
138C7×C8—82no—
139C22×Q8C2×C4×C711yescharacteristic
140C22×D4C7×D411yescharacteristic
141C23×C4C7×D412yes—
142C2×M16—22no—
143C22×C8—24no—
144C4×Q8—22no—
145C4×Q8—22no—
146C4×D4—22no—
147C4×D4—22no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4C2×C4×C711yescharacteristic
152C2×C4⋊C4C7×D411yescharacteristic
153C2×C22⋊C4—22no—
154C2×C22⋊C4—22no—
155C2×C22⋊C4C2×C4×C712yes—
156C2×C42—21no—
157C2×C42C23×C711yescharacteristic
158C4⋊C8—22no—
159C4⋊C8—22no—
160C4⋊C8—22no—
161#100—42no—
162C22⋊C8—24no—
163C22⋊C8—22no—
164C4×C8C7×D414yes—
165#95—22no—
166#95—21no—
167#95C2×C4×C712yes—
168C22×C7—21no—
169C22×C7—21no—
170C22×C7—24no—
171C22×C7—44no—
172C22×C7—42no—
173C22×C7—42no—
174C22×C7—82no—
175C22×C7#38611yescharacteristic
176C22×C7C2×#10311yescharacteristic
177C22×C7#41611yescharacteristic
178C4×C7—22no—
179C4×C7—21no—
180C4×C7—21no—
181C4×C7—42no—
182C4×C7—42no—
183C4×C7—82no—
184C4×C7—81no—
185C4×C7#46512yes—
186C4×C7#46712yes—
187C24C7×C22⋊C412yes—
188C2×Q8—22no—
189C2×Q8—42no—
190C2×D4—22no—
191C2×D4—22no—
192C2×D4C7×SD1612yes—
193C2×D4C7×Q1612yes—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—21no—
199C22×C4—82no—
200C22×C4C7×C22⋊C412yes—
201C22×C4C22×C4×C711yescharacteristic
202C22×C4C2×C7×D411yescharacteristic
203C22×C4C2×C7×D411yescharacteristic
204M16—42no—
205M16—42no—
206C2×C8—24no—
207C2×C8—42no—
208C2×C8—84no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—82no—
215C22⋊C4—24no—
216C22⋊C4—44no—
217C22⋊C4—82no—
218C42—42no—
219C42C2×C7×D412yes—
220C42C7×#4112yes—
221C2×C7—21no—
222C2×C7—21no—
223C2×C7—44no—
224C2×C7#189111yescharacteristic
225C2×C7#189211yescharacteristic
226C2×C7#191111yescharacteristic
227C23—22no—
228C23—22no—
229C23—42no—
230C23—42no—
231C23C7×#10314yes—
232C23C2×C7×C22⋊C411yescharacteristic
233Q8—24no—
234Q8—42no—
235D4—24no—
236D4—24no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—44no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—82no—
252C2×C4C4×C7×D412yes—
253C2×C4C7×#12011yescharacteristic
254C2×C4C7×#12112yes—
255C2×C4C7×#12311yescharacteristic
256C2×C4C2×C7×SD1611yescharacteristic
257C2×C4C2×C7×Q1611yescharacteristic
258C2×C4C7×#13512yes—
259C8—44no—
260C8—82no—
261C7#948311yescharacteristic, direct product factor, Sylow
262C22—21no—
263C22—21no—
264C22—24no—
265C22—44no—
266C22—42no—
267C22—42no—
268C22—82no—
269C22C7×#38611yescharacteristic
270C22C2×C7×#10311yescharacteristic
271C22C7×#41611yescharacteristic
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—42no—
277C4—82no—
278C4—81no—
279C4C7×#46512yes—
280C4C7×#46712yes—
281C2—21no—
282C2—21no—
283C2—44no—
284C2C7×#189111yescharacteristic
285C2C7×#189211yescharacteristic
286C2C7×#191111yescharacteristic
subgroupG/H
center, socleC22×C7#386
commutatorC22×C4C22×C4×C7
Frattini, cosocleC2×C42C23×C7
prime radicalC22×C7×D4D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. C7×#1487C2semidirect
5. C7×#1286C2semidirect
21. #9483C7direct (N × H)
54. #1487C2×C7semidirect
55. #1286C2×C7semidirect
261. C7#9483direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C7×#29722
C7×#25802
C7×#18002
C7×#14872
C7×#12862
#94837